Semi-Markov and Markov Renewal Processes

Abstract

State space is usually defined by the number of units that are working satisfactorily. As far as the applications to reliability theory is concerned, we consider only a finite number of states, contrast with a queueing theory. We mention only the theory of stationary Markov processes with a finite-state space. It is shown that transition probabilities, first-passage distributions, and renewal functions are given by forming renewal equations. Furthermore, some limiting properties are summarized when all states communicate.